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Achieving high-precision measurements on near-term quantum devices is critical for advancing quantum computing applications. In this paper, we explore several practical techniques to enhance measurement accuracy using randomized measurements, focusing on minimizing shot overhead, circuit overhead, measurement noise, and time-dependent measurement noise. Our approach leverages locally biased random measurements to reduce shot overhead, in addition to repeated settings and parallel quantum detector tomography to reduce circuit overhead and mitigate measurement noise. Additionally, we employ a blended scheduling technique to mitigate time-dependent measurement noise. We demonstrate the effectiveness of these techniques through a case study on the molecular energy estimation of the BODIPY molecule using the Hartree-Fock state on an IBM Eagle r3 computer, showcasing significant improvements in measurement precision. These strategies pave the way for more reliable and accurate quantum computations, particularly in applications requiring precise molecular energy calculations., Comment: 15 pages, 8 figures

By leveraging the Variational Quantum Eigensolver (VQE), the ``quantum equation of motion" (qEOM) method established itself as a promising tool for quantum chemistry on near term quantum computers, and has been used extensively to estimate molecular excited states. Here, we explore a novel application of this method, employing it to compute thermal averages of quantum systems, specifically molecules like ethylene and butadiene. A drawback of qEOM is that it requires measuring the expectation values of a large number of observables on the ground state of the system, and the number of necessary measurements can become a bottleneck of the method. In this work we focus on measurements through informationally complete positive operator-valued measures (IC-POVMs) to achieve a reduction in the measurements overheads. We show with numerical simulations that the qEOM combined with IC-POVM measurements ensures a satisfactory accuracy in the reconstruction of the thermal state with a reasonable number of shots., Comment: 7 pages, 9 figures

Characterization of noise in current near-term quantum devices is of paramount importance to fully use their computational power. However, direct quantum process tomography becomes unfeasible for systems composed of tens of qubits. A promising alternative method based on tensor networks was recently proposed [Nat. Commun. 14, 2858 (2023)]. In this paper, we adapt it for the characterization of noise channels on near-term quantum computers and investigate its performance thoroughly. In particular, we show how experimentally feasible tomographic samples are sufficient to accurately characterize realistic correlated noise models affecting individual layers of quantum circuits, and study its performance on systems composed of up to 20 qubits. Furthermore, we combine this noise characterization method with a recently proposed noise-aware tensor network error mitigation protocol for correcting outcomes in noisy circuits, resulting accurate estimations even on deep circuit instances. This positions the tensor-network-based noise characterization protocol as a valuable tool for practical error characterization and mitigation in the near-term quantum computing era., Comment: Updated version matching publication (minor modifications, added section on SPAM errors)